No, turkeys and emus came from dinosaurs. I'm pretty sure dinosaurs are an impurity in it.
Peat, Coal, oil and gas are related.
Also not all plastics are petrochemical based. You can make plastics from various organic sources. Though Cellulose Nitrate film (which can be made from cotton) isn't used now. /me checks wikipedia
https://en.wikipedia.org/wiki/Nitrocellulose
Yep, scary stuff and yet they made billiard balls from it for a while. It's why film projection rooms were the original no-smoking zone. Then they invented a safer film.
More curiously not all natural rubber from latex is from the "rubber tree". All dandelions and maybe some lettuce can produce it. The Russians are alleged to have a particularly good variety of dandelion for rubber production.